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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 574.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
574.d1 | 574b2 | \([1, 1, 0, -2221, 29181]\) | \(1212480836738137/310100175392\) | \(310100175392\) | \([2]\) | \(960\) | \(0.91449\) | |
574.d2 | 574b1 | \([1, 1, 0, -2061, 35165]\) | \(968917714969177/100803584\) | \(100803584\) | \([2]\) | \(480\) | \(0.56792\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 574.d have rank \(1\).
Complex multiplication
The elliptic curves in class 574.d do not have complex multiplication.Modular form 574.2.a.d
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.